Pedro has created the function f(x) =the quantity of 4x minus 3, divided by 2 to represent the number of assignments he has completed, where x represents the number of weeks in the course. Pedro discovers that, using the inverse function to solve for x = 30, he can predict when he will have 30 assignments completed. Explain to Pedro how to accomplish this, using complete sentences.
Answers
Given : Pedro has created the function f(x) = (4x - 3)/2 to represent the number of assignments he has completed, where x represents the number of weeks
To Find : using the inverse function to solve for x = 30, predict when he will have 30 assignments completed.
Solution:
x = number of weeks
f(x) = number of assignments
f(x) = (4x - 3)/2
=> 2 f(x) = 4x - 3
=> 2 f(x) + 3 = 4x
=> (2 f(x) + 3 )/4 = x
=> f⁻¹(x) = (2x + 3)/4
x = 30
=> f⁻¹(30) = (2 * 30 + 3)/4
=> f⁻¹(30) = 63/4
63/4 weeks he will take to complete 30 assignments
15.75 weeks
Verification
f(x) = (4x - 3)/2
=> f(63/4) = ( 4 *(63/4) - 3) /2
=> f(63/4) = (63 - 3)/2
=> f(63/4) = (60)/2
=> f(63/4) = 30
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